Part 2: Mechanical Waves
Chapter 17: Sound Waves
Reading assignment: Chapter 17.1 to 17.4
Homework (not due, practice for exam)
Problems:
2, 5, 9, 35, 43
• Sound waves are the most important example of longitudinal
waves.
• They can travel through any material, except vacuum (no one
can hear you scream in outer space).
• Speed of sound depends on material (and temperature)
Check out the spectral analyzer: http://www.qsl.net/dl4yhf/spectra1.html#download
Announcements
• Final exam
– Monday, Dec. 10, 2:00 pm – 5:00 pm
– No later, alternative date!
– Comprehensive; chapters 1-17 (as far was we get).
– Same format as midterms.
– Go through all exams and practice exams, HW, in class problems,
concepts.
– Practice exams for material after midterm 2 will be posted.
– Extended office hours, Sunday, 1:00 pm – 3:00 pm.
Sound Waves
Sound waves are longitudinal waves.
They consist of compressed and rarified regions of gas (medium)
We can hear (audible) frequencies from about 20 Hz (low) to 15,000 Hz (high).
Infrasonic “sound” waves: below ~ 20 Hz
Ultrasonic sound waves: above ~ 15,000 Hz
Sound
- is a wave (sound wave)
- Rarefied and compressed regions
-  high pressue/low pressure regions
- Longitudinal wave
- air molecules move back and forth
Sound waves, hearing and the ear
Image: http://www.innerbody.com/anim/ear.html
Movie: http://www.youtube.com/watch?v=ahCbGjasm_E
Notes and their
fundamental
frequency
Octaves: Frequency
doubles for each tone
Speed of Sound Waves
In gas and liquids:
v
In solids:
B
v

Y

Y… Young’s modulus (see Chapter 12.4)
B… Bulk modulus of medium (see Chapter 12.4)
…density of material
Bulk modules
determines the volume
change of an object due
to an applied pressure P.
volume stress
F/A
P
B


volume strain V / Vi V / Vi
Young’s modules
determines the length
change of an object
due to an applied force
F.
tensile stress
F/A
Y

tensile strain L / Li
Speed of Sound in various materials
Speed of sound in air : v  (331 m/s )  1 
TC … air temperature in degrees Celsius
TC
273C
Black board example 17.1
Lightning strikes 10 miles
(16090 m) away from you.
(a) How long does it take the light to get to you?
(b) How long does it take the sound of thunder to get to you (Temp= 20ºC = 68F ).
(c) How far does the sound travel in one second?
Periodic sound waves.
(A constant tone is a periodic sound wave)
Condensation:
Regions of compressed gas.
(high pressure)
Rarefactions:
Regions of rarefied gas.
(low pressure)
Distance between two compressed regions: Wavelength l
Periodic sound waves.
Displacement of small volume element:
sx, t   smax coskx  t 
Pressure variation:
Px, t   Pmax sin kx  t 
Doppler effect
When heading into waves: Frequency becomes higher.
When heading away from waves: Frequency becomes lower.
Doppler effect
When heading into waves: Frequency becomes higher.
When heading away from waves: Frequency becomes lower.
O… observer (listener)
S… Source (of wave)
Doppler effect
Moving observer
Moving source
 vO 
f '  1   f
v 


 1
f ' 
 1  vS

v



f



+… observer moving toward source
+… source moving away from observer
- … observer moving away from source
- … source moving towards observer
O … observer;
S … source;
If both, observer and source are moving:
v … speed of sound
 vO
1
v
f ' 
 1  vS

v



f



Black board example 17.3
Homework 17.33
A commuter train passes a
passenger platform at a
constant speed of 40 m/s.
The train horn is sounded
at its characteristic
frequency of 320 Hz.
(Use v = 343 m/s for the
speed of sound.)
(a) What change in frequency is detected by a person on the
platform as the train passes?
(b) What wavelength is detected by a person on the platform as the
train approaches?
Shock waves
When the speed of the
object, vO, exceeds the
wave speed, v.
v t
v
sin  

vO  t vO
The ratio vO/v is called the Mach number.
For sound: Mach 3 means 3x the speed of sound.